When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables.
If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y).
If the graphs do not cross anywhere (for example, parallel lines) then there is no solution.
If the graphs of two lines end up being the same line, then there are an infinite number of solutions.
You must know how to graph a line in order to use this method.
I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.
josh hutcherson
This looks like a question from a Virtual School course - please ask you teacher for help and use the examples in the lesson.
Assuming you want to plot two linear equations, you plot the graphs of both, and look where they intersect. One way to plot a linear equation is to convert it to the form y = ax + b; in this case, a is the slope, and b is the y-intercept - the coordinates where the line crosses the y-axis.
Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).
I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.
The answer depends on whether they are linear, non-linear, differential or other types of equations.
josh hutcherson
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.
There are no disadvantages. There are three main ways to solve linear equations which are: substitution, graphing, and elimination. The method that is most appropriate can be found by looking at the equation.
7-3
This looks like a question from a Virtual School course - please ask you teacher for help and use the examples in the lesson.
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
You simplify the brackets first and then you will have linear equations without brackets!
To solve linear equations, you always use the inverse operations
Assuming you want to plot two linear equations, you plot the graphs of both, and look where they intersect. One way to plot a linear equation is to convert it to the form y = ax + b; in this case, a is the slope, and b is the y-intercept - the coordinates where the line crosses the y-axis.
Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).